What is the Greatest Common Factor of 638 and 654?

Greatest common factor (GCF) of 638 and 654 is 2.

GCF(638,654) = 2

We will now calculate the prime factors of 638 and 654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 638 and 654.

How to find the GCF of 638 and 654?

We will first find the prime factorization of 638 and 654. After we will calculate the factors of 638 and 654 and find the biggest common factor number .

Step-1: Prime Factorization of 638

Prime factors of 638 are 2, 11, 29. Prime factorization of 638 in exponential form is:

638 = 2¹ × 11¹ × 29¹

Step-2: Prime Factorization of 654

Prime factors of 654 are 2, 3, 109. Prime factorization of 654 in exponential form is:

654 = 2¹ × 3¹ × 109¹

Step-3: Factors of 638

List of positive integer factors of 638 that divides 638 without a remainder.

1, 2, 11, 22, 29, 58, 319

Step-4: Factors of 654

List of positive integer factors of 654 that divides 638 without a remainder.

1, 2, 3, 6, 109, 218, 327

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 638 and 654. The biggest common factor number is the GCF number.
So the greatest common factor 638 and 654 is 2.

Also check out the Least Common Multiple of 638 and 654